Well, considering that 0 IS a finite number that pretty much means that you consider all numbers as "a lot alike"!
One of the most basic semantic conventions is that when a particular word has an established usage, that anyone using that word unqualified means that usage.To be fair, you pretended you knew what *I* was saying when I said what I did
Reality? What does that have to do with anything?I never made any representation that I believed in your version of reality
General purpose dictionaries good for defining words in every day usage. They're notoriously bad at defining technical words. (After all, their purpose is the former, not the latter)Plus, given the definition I provided from a (possibly less than reputable) third party, it seems a fair enough issue to give me the benefit of the doubt.
Depends on the context. When dealing with sets with an ordering and contain integers, by far the most typical definition is:How would you define "finite", exactly?
Every number has its own pecularities.Zero is certainly a peculiar finite number, if you consider it to be such. No sign, no multiplicative inverse,
Nononono. First off, it can only possibly have any relation to the idea of quantity in the particular case we are using a number to quantify something. Quantification is not inherent to the mathematical notion of number.and semantically meaning the absence of quantity.
I would imagine that one could also go off into fantastical reveries (much like has been done with infinity)
Nonzero. :tongue: (Actually, zero is an infinitessimal. All other infinitessimals would be nonzero)What are infinitesimals if not a kind of zero?
You claim to be a CS professor... what if I came into your class and tried to tell you that 1 is not O(x), or that the halting problem was computable? And then when you corrected me, I simply accused you of mindlessly 'parroting conventional wisdom'?Anyway, done with this rant. Jeez, you guys take things so personally sometimes. It's not about trying to say you're suckers for seeing things one way.
How so?...Infinity is a special class of number...
Just what do you mean by "right"?It seems dogmatic, to me, to pretend that the current definition is necessarily the right one.
Of course. For example, each of the definitions I gave earlier -- "finite set", "finite cardinal number", "finite extended real number", "finite point of the projective plaine" -- those are all different definitions of different things.Other definitions are sometimes possible
Final word??What I meant to say, and I apologize if this was actually unclear, is that sometimes the currently accepted definition is not the final word in the definition.
This is very clear. Here, you are advocating the ideas that:How can you call 0 finite?
Have you ever given it any thought, or are you just parroting conventional wisdom?
As in your previous empty blather?Perhaps a better, more useful definition is possible.
how considerate of you.I think I'm done with this thread.